Phase relations and equation-of-state of aluminous Mg-silicate perovskite and implications for Earth's lower mantle

We have investigated the effect of Al³⁺ on the room-temperature compressibility of perovskite for stoichiometric compositions along the MgSiO₃-AlO_1.5 join with up to 25 mol% AlO_1.5. Aluminous Mg-perovskite was synthesized from glass starting materials, and was observed to remain a stable phase in the range of ∼30-100 GPa at temperatures of ∼2000 to 2600 K. Lattice parameters for orthorhombic (Pbnm) perovskite were determined using in situ X-ray diffraction at SPring8, Japan. Addition of Al³⁺ into the perovskite structure increases orthorhombic distortion and unit cell volume at ambient conditions (V₀). Compression causes anisotropic decreases in axial length, with the a axis more compressive than the b and c axes by about 25% and 3%, respectively. The magnitude of orthorhombic distortion increases with pressure, but aluminous perovskite remains stable to pressures of at least 100 GPa. Our results show that substitution of Al³⁺ causes a mild increase in compressibility, with the bulk modulus (K₀) decreasing at a rate of −67±35 GPa/X_Al. This decrease in K₀ is consistent with recent theoretical calculations if essentially all Al³⁺ substitutes equally into the six- and eight-fold sites by charge-coupled substitution with Mg²⁺ and Si⁴⁺. In contrast, the large increase in compressibility reported in some studies with addition of even minor amounts of Al is consistent with substitution of Al³⁺ into six-fold sites via an oxygen-vacancy forming substitution reaction. Schematic phase relations within the ternary MgSiO₃-AlO_1.5-SiO₂ indicate that a stability field of ternary defect Mg-perovskite should be stable at uppermost lower mantle conditions. Extension of phase relations into the quaternary MgSiO₃-AlO_1.5-FeO_1.5-SiO₂ based on recent experimental results indicates the existence of a complex polyhedral volume of Mg-perovskite solid solutions comprised of a mixture of charge-coupled and oxygen-vacancy Al³⁺ and Fe³⁺ substitutions. Primitive mantle with about 5 mol% AlO_1.5 and an Fe³⁺/(Fe³⁺+Fe²⁺) ratio of ∼0.5 is expected to be comprised of ferropericlase coexisiting with Mg-perovskite that has a considerable component of Al³⁺ and Fe³⁺ defect substitutions at conditions of the uppermost lower mantle. Increased pressure may favor charge-coupled substitution reactions over vacancy forming reactions, such that a region could exist in the lower mantle with a gradient in substitution mechanisms. In this case, we expect the physical and transport properties of Mg-perovskite to change with depth, with a softer, probably more hydrated, defect dominated Mg-perovskite at the top of the lower mantle, grading into a stiffer, dehydrated, charge-coupled substitution dominated Mg-perovskite at greater depth.     

Synthesis and crystal-chemical characterization of MgSiO3 perovskite

The orthorhombic MgSiO₃ perovskite has been synthesized with the aid of a double-stage split-sphere-type high-pressure apparatus at about 280 kbar and 1000°C. The unit cell dimensions are: a = 4.7754(3)Å, b = 4.9292(4)Å and c = 6.8969(5)Å with the probable space group Pbnm. Calculated density is 4.108 g cm^?3. Crystal structure determination has been carried out by means of both the geometrical simulation (DLS) technique and the ordinary powder X-ray analysis. The results indicate that the MgSiO₃ perovskite is closer to the ideal perovskite than ScAlO₃ perovskite.     

Post-ilmenite phases of silicates and germanates

MgSiO₃, ZnSiO₃, MgGeO₃, MnGeO₃, and ZnGeO₃ are the only silicates and germanates known to crystallize in the ilmenite-like structure at high pressures and high temperatures. With the exception of the zinc compounds, the above-mentioned ilmenites have all been found to transform to the orthorhombic modification of the perovskite structure at higher pressures. The ilmenite phase of ZnSiO₃, on the other hand, transforms to its component oxide mixture with the rocksalt and rutile structures, whereas ZnGeO₃ (ilmenite) transforms first to an as yet undetermined orthorhombic phase and then to its component oxide mixture. The direct transformation from the ilmenite to perovskite structures observed in the metasilicates and metagermanates is consistent with all other reported high-pressure post-ilmenite phases (CdTiO₃, CdSnO₃, MnVO₃, and (Fe,Mg)TiO₃). The observation of the ilmenite-perovskite transformation in MgSiO₃ and its solid solutions towards Al₂O₃ suggests that MgO (rocksalt) + SiO₂ (rutile) + Al₂O₃ (corundum) is not a stable mineral assemblage for the earth's lower mantle.     

High-pressure phases of Co2GeO4, Ni2GeO4, Mn2GeO4 and MnGeO3: implications for the germanate-silicate modeling scheme and the Earth's mantle

In a diamond-anvil press coupled with YAG laser heating, the spinels of Co₂GeO₄ and Ni₂GeO₄ have been found to disproportionate into their isochemical oxide mixtures at about 250 kbar and 1400–1800°C in the same manner as their silicate analogues. At about the same P-T conditions MnGeO₃ transforms to the orthorhombic perovskite structure (space group Pbnm); the lattice parameters at room temperature and 1 bar are a₀ = 5.084 ± 0.002, b₀ = 5.214 ± 0.002, and c₀ = 7.323 ± 0.003Å with Z = 4 for the perovskite phase. The zero-pressure volume change associated with the ilmenite-perovskite phase transition in MnGeO₃ is ?6.6%. Mn₂GeO₄ disproportionates into a mixture of the perovskite phase of MnGeO₃ plus the rocksalt phase of MnO at P = 250kbar and T = 1400–1800°C. The concept of utilizing germanates as high-pressure models for silicates is valid in general. The results of this study support the previous conclusion that the lower mantle comprises predominantly the orthorhombic perovskite phase of ferromagnesian silicate.     

The high-pressure phases of MgSiO3

The high-pressure and temperature phase transformations of MgSiO₃ have been investigated in a diamond-anvil cell coupled with laser heating from 150 to 300 kbar at 1000–1400°C. X-ray diffraction study of the quenched samples reveals that the sequence of phase transformations for this compound is clinoenstatite → β-Mg₂SiO₄ plus stishovite → Mg₂SiO₄(spinel) plus stishovite → ilmenite phase → perovskite phase with increasing pressure. The hexagonal form of MgSiO₃ observed by Kawai et al. is demonstrated to have the ilmenite structure and the “hexagonal form” of MgSiO₃ observed by Ming and Bassett is shown to be predominantly the orthorhombic perovskite phase plus the ilmenite phase. The mixture of oxides, periclase plus stishovite, reported by Ming and Bassett was not observed in this study. The very wide stability field for the ilmenite phase of MgSiO₃ found in this study suggests that this phase is of importance in connection with the observed rapid increase of velocity in the transition zone of the earth's mantle. On the basis of the extremely dense-packed structure of the perovskite phase of MgSiO₃, this phase should be the most important component for the lower mantle.     

A relationship between phonon conductivity and seismic parameter Φ for silicate minerals

Summary The relationship between the phonon conductivity at room temperature (K _N ) and the seismic parameter () for silicate minerals is suggested. The considerations are based on the Debye model of thermal energy transport phenomena in solids and on the seismic equation of state for silicates and oxides given byAnderson (1967). The semiempirical relationship is the formK _N = 0.43^0.82 where is in km²/s² andK _N in mcal/cm s K, and the empirical relationship isK _N =(0.528±0.006) –(8.18±2.11). The laboratory data on thermal and elastic properties for several silicates were taken fromHorai andSimmons (1970).     

Elasticity of single-crystal SmAlO3, GdAlO3 and ScAlO3 perovskites

The adiabatic single-crystal elastic moduli of SmAlO₃, GdAlO₃ and ScAlO₃, all with the orthorhombic perovskite structure, have been measured by Brillouin spectroscopy under ambient conditions. These 3 compounds display various degrees of crystallographic distortion from the ideal cubic perovskite structure. We find that longitudinal moduli in directions parallel to the axes of a pseudocubic subcell are nearly equal and insensitive to distortions of the crystal structure from cubic symmetry, whereas, the moduli C₁₁ and C₂₂, parallel to the orthorhombic axes, display pronounced anisotropy with the exception of ScAlO₃. The shear moduli also correlate with distortion from cubic symmetry, as measured by rotation, or tilt angles, of the AlO₆ octahedra. Our data support the observations of Liebermann et al. that perovskite-structure compounds define consistent elasticity trends relating bulk modulus and molar volume, and sound speed and mean atomic weight. These relationships have been used to estimate bulk and shear moduli for the high-pressure polymorphs of CaSiO₃ and MgSiO₃ with the perovskite structure.     

Elasticity of aluminate,titanate, stannate and germanate compounds with the perovskite structure

Ultrasonic data for the velocities of a large number of perovskite-structure compounds have been determined as a a function of pressure to 6 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 100 kbar in solid-media devices: ScAlO₃, GdAlO₃, SmAlO₃, EuAlO₃, YAlO₃, CdTiO₃, CdSnO₃, CaSnO₃ and CaGeO₃. The elasticity data for these orthorhombic and cubic perovskites define systematic patterns on bulk modulus (K_S)-volume (V_O) and bulk sound velocity (υ_φ—mean atomic weight (M) diagrams which are insensitiv to the details of cation chemistry and crystallographic structure. These isostructural trends are used to estimate K_S = 2.5 ± 0.3 Mbar and υ_φ = 7.9 ± 0.4 km/s for the perovskite polymorph of MgSiO₃. On a Birch diagram of veloc vs. density, the perovskite data define linear trends which lead to erroneous estimates of velocity for MgSiO₃ unless specific account is taken of ionic radius effects in isomorphic substitutions.     

Oxygen isotope fractionation in mantle minerals

The increment method is adopted to calculate oxygen isotope fractionation factors for mantle minerals, particularly for the polymorphic phases of MgSiO₃ and Mg₂SiO₄. The results predict the following sequence of¹⁸O-enrichment:pyroxene (Mg, Fe, Ca)₂Si₂O₆>olivine (Mg, Fe)₂SiO₄ > spinel (Mg, Fe)₂SiO₄> ilmenite (Mg, Fe, Ca) SiO₃>perovskite (Mg, Fe, Ca) SiO₃. The calculated fractionations for the calcite-perovskite (CaTiO₃) System are in excellent agreement with the experimental calibrations. If there would be complete isotopic equilibration in the mantle, the spinel-structured silicates in the transition zone are predicted to be enriched in¹⁸O relative to the perovskite-structured silicates in the lower mantle but depleted in¹⁸O relative to olivines and pyroxenes in the upper mantle. The oxygen isotope layering of the mantle might result from differences in the chemical composition and crystal structure of mineral phases at different mantle depths. Assuming isotopic equilibrium on a whole earth scale, the chemical structure of the Earth’s interior can be described by the following sequence of¹⁸O-enrichment:upper crust>lower crust>upper mantle>transition zone>lower mantle>core. Project supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences.     

Elasticity of (Mg, Fe)(Si, Al)O3-perovskite at high pressure

The most abundant mineral on Earth has a perovskite crystal structure and a chemistry that is dominated by MgSiO₃ with the next most abundant cations probably being aluminum and ferric iron. The dearth of experimental elasticity data for this chemically complex mineral limits our ability to calculate model seismic velocities for the lower mantle. We have calculated the single crystal elastic moduli (c_ij) for (Mg, Fe^3 +)(Si, Al)O₃ perovskite using density functional theory in order to investigate the effect of chemical variations and spin state transitions of the Fe³⁺ ions. Considering the favored coupled substitution of Mg²⁺-Si^4 + by Fe³⁺-Al³⁺, we find that the effect of ferric iron on seismic properties is comparable with the same amount of ferrous iron. Ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. Substitution of Fe³⁺ for Al³⁺, giving rise to an Fe/Mg ratio of 6%, causes 1.8% lower longitudinal velocity and 2.5% lower shear velocity at ambient pressure and 1.1% lower longitudinal velocity and 1.8% lower shear velocity at 142 GPa. The spin state of the iron for this composition has a relatively small effect (< 0.5% variation) on both bulk modulus and shear modulus.     

A thin film approach for producing mineral diffusion couples

Few diffusion coefficient values have been measured for silicate minerals at pertinent geologic conditions because of experimental restrictions. Until recently, analysis of diffusion couples was conducted principally with electron microprobes which have rather poor spatial resolution (micrometer scale). Ion microprobe analyses, however, eliminate many of the previous experimental restrictions; in depth profile mode they have excellent spatial resolution (tens of angstroms) and diffusion couples can be analyzed normal to the interface. Diffusion couples analyzed by ion microprobe must be well-defined and uniform; previous methods using solution precipitates to form the diffusion couples were heterogeneous and had limited success. A new approach, the thermal evaporation of²⁵MgO under high vacuum onto a crystalline substrate (oxide, silicate), produces a 1000 Å thick²⁵MgO _x (x<1) thin film. This method yields an excellent diffusion couple for low-temperature diffusion experiments. Diffusion anneal experiments using this approach for garnet provide a Mg self-diffusion coefficient ofD=0.60±0.09×10^–21 m²/s at 1000°C (logFO₂=–11.3,P=1 atm,X _Almandine=0.24).     

Structure constraints and instability leading to the post-perovskite phase transition of MgSiO3

Recent experience with Rietveld refinement of structural analogues and literature surveys, suggests anion–anion repulsion limits the stability of the perovskite phase, including in the MgSiO₃ perovskite to post-perovskite transition. Assuming rigid octahedral coordination, still to be tested experimentally, the critical point where intra- and inter-octahedral anion–anion distances are equal provides a useful metric for predicting the pressure of the perovskite/post-perovskite transition and the Clapeyron slope of the phase boundary, once pressure and temperature derivatives of relevant structure parameters are known. The inter-octahedral anion–anion distances and the polyhedral volume ratio are rigorously formulated as a function of octahedral rotation in this work, assuming the orthorhombic (Pbnm) perovskite structure, where regular octahedra share each corner and conform to the in- and anti-phase rotation schemes designated by space group symmetry. These mathematical expressions are consistent with structure data from 70 perovskite-structured materials surveyed in the literature at ambient as well as extreme conditions and define structure constraints, such as the minimum polyhedral volume ratio, which must be reached before the phase transition to the post-perovskite structure-type can proceed. The formalism we present is general for perovskite (Pbnm) and dependent on the accuracy with which structures can be determined from, sometimes compromised, high pressure diffraction data.     

High-pressure synthesis of ZnSiO3 ilmenite

High-pressure phase relations in ZnSiO₃ and Zn₂SiO₄ were investigated at about 1000°C and in the pressure range of 100–500 kbar, using a double-staged split-sphere type of high-pressure apparatus.Clinopyroxene-type ZnSiO₃ transforms directly into a polymorph with the ilmenite structure at 120 kbar. The hexagonal unit cell dimensions of the ZnSiO₃ ilmenite are determined to be $\text{a = 4.746 ± 0.001}\text{A}\text{?}\text{and}\text{c = 13.755 ± 0.002}\text{A}\text{?}$ under ambient conditions.The following reactions are also recognized at about 1000°C:

and:

The stabilities of silicate ilmenites, especially the absence of ilmenite of transition metal silicate composition, is discussed. It is pointed out that data on phase relations in zinc silicates may be informative for the consideration on those in magnesium silicates under very high pressures. It is suggested that the silicate ilmenite may be a major constituent in the lower mantle.     

Synthesis of a new high-pressure ohase of tin dioxide and some geophysical implications

Tin dioxide (SnO₂) in the rutile structure as starting material has been found to transform to the orthorhombic α-PbO₂ structure (S.G. Pbcn) at about 155 kbar and 1000–1400°C when compressed in a diamond-anvil cell and heated by irradiation with a YAG laser. The lattice parameters at room temperature and 1 bar are $\text{a}{}_{\mathrm{<mtext>o</mtext>}}\text{= 4.719 ± 0.002, b}{}_{\mathrm{<mtext>o</mtext>}}\text{= 5.714 ± 0.002,}\text{and}\text{c}{}_{\mathrm{<mtext>o</mtext>}}\text{= 5.228 ± 0.002}\text{A}\text{?}\text{with}\text{Z = 4}$ for the orthorhombic form of SnO₂, which is 1.5% more dense than the rutile form. Crystal-chemical arguments suggest that stishovite (SiO₂) may also transform to the α-PbO₂ structure at elevated pressure and temperature with an increase in zero-pressure density of about 2–3%. Mineral assemblages containing the orthorhombic SiO₂ are unstable relative to those containing the perovskite MgSiO₃ under lower-mantle conditions.     

Spin state of ferric iron in MgSiO3 perovskite and its effect on elastic properties

Recent studies have indicated that a significant amount of iron in MgSiO₃ perovskite (Pv) is Fe³⁺ (Fe³⁺/ΣFe = 10–60%) due to crystal chemistry effects at high pressure (P) and that Fe³⁺ is more likely than Fe²⁺ to undergo a high-spin (HS) to low-spin (LS) transition in Pv in the mantle. We have measured synchrotron Mössbauer spectroscopy (SMS), X-ray emission spectroscopy (XES), and X-ray diffraction (XRD) of Pv with all iron in Fe³⁺ in the laser-heated diamond-anvil cell to over 100 GPa. Fe³⁺ increases the anisotropy of the Pv unit cell, whereas Fe²⁺ decreases it. In Pv synthesized above 50 GPa, Fe³⁺ enters into both the dodecahedral (A) and octahedral (B) sites approximately equally, suggesting charge coupled substitution. Combining SMS and XES, we found that the LS population in the B site gradually increases with pressure up to 50–60 GPa where all Fe³⁺ in the B site becomes LS, while Fe³⁺ in the A site remains HS to at least 136 GPa. Fe³⁺ makes Pv more compressible than Mg-endmember below 50 GPa because of the gradual spin transition in the B site together with lattice compression. The completion of the spin transition at 50–60 GPa increases bulk modulus with no associated change in density. This elasticity change can be a useful seismic probe for investigating compositional heterogeneities associated with Fe³⁺.     

Orthorhombic perovskite phases observed in olivine,pyroxene and garnet at high pressures and temperatures

Ferromagnesian silicate olivines, pyroxenes and garnets with Mg/(Mg + Fe)?0.3 (molar) have been found to transform to high-pressure phases characterized by the orthorhombic perovskite structure when compressed to pressures above 250 kbar in a diamond-anvil press and heated to temperatures above 1,000°C with a YAG laser. The zero-pressure density of the perovskite phase of (Mg,Fe)SiO₃ is about 3–4% greater than that of the close-packed oxides, rocksalt plus stishovite. For (Mg,Fe)₂SiO₄ compounds, the perovskite plus rocksalt phase assemblage is 2–3% denser than the mixed oxides. The experimental synthesis of such high-density perovskite phases in olivine, pyroxene and garnet compounds suggests that (Mg,Fe)SiO₃-perovskite is the dominant mineral phase in the earth's lower mantle.     

High-pressure phase transformations and isothermal compression in CaTiO3 (perovskite)

A polycrystalline CaTiO₃ (perovskite) was investigated under static pressures up to 38 GPa and temperatures up to 1000°C by using a diamond anvil pressure cell, a YAG laser, and the ruby fluorescence pressure calibration system. In situ x-ray diffraction data reveal that at room temperature, the orthorhombic CaTiO₃(I) transforms into a hexagonal CaTiO₃(II) at ∼ 10 GPa with a volume of change of 1.6%. At 1000°C, the orthorhombic CaTiO₃(I) first transforms into a tetragonal CaTiO₃(III) at 8.5 GPa and then transforms further into a hexagonal CaTiO₃(II′) at ∼ 15 GPa with molar volume changes of 0% and 1.6%, respectively. All three high-pressure polymorphs found in this study are nonquenchable.Isothermal compressibility of the orthorhombic CaTiO₃ was derived from measurements under truly hydrostatic environments (i.e., ⩽ 10.4 GPa). By assuming K^′₀ = 5.6 obtained ultrasonically on SrTiO₃ perovskite, the value of the bulk modulus (K₀) was calculated with the Birch-Murnaghan equation to be 210 ± 7 GPa.     

Computation of Ray Amplitudes in Inhomogeneous Media with Curved

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W ₀ and the geopotential scale factor R ₀ = GM÷W ₀ (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W ₀ = (62 636 856.161 ± 0.002) m²s^-2, R ₀ = (6 363 672.5448 ± 0.0002) m. The actual accuracy is limited by the altimeter calibration error (2–3 cm) and it is conservatively estimated to be about ± 0.5 m²s^-2 (± 5 cm). The differences between the yearly mean sea surface (MSS) levels came out as follows: 1993–1994: –(1.2 ± 0.7) mm, 1994–1995: (0.5 ± 0.7) mm, 1995–1996: (0.5 ± 0.7) mm, 1996–1997: (0.1 ± 0.7) mm, 1997–1998: –(0.5 ± 0.7) mm, 1998–1999: (0.0 ± 0.7) mm and 1999–2000: (0.6 ± 0.7) mm. The corresponding rate of change in the MSS level (or R ₀) during the whole period of 1993–2000 is (0.02 ± 0.07) mm÷y. The value W ₀ was found to be quite stable, it depends only on the adopted GM, and the volume enclosed by surface W = W ₀. W ₀ can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W ₀ is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W ₀ provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W ₀, the semi-major axis a of the Earth's general ellipsoid can easily be derived. However, an a priori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W ₀ in the least squares sense and an ellipsoid which has the global geopotential average equal to W ₀. It is demonstrated that both a-values are practically equal to the value obtained by the Pizzetti's theory of the level ellipsoid: a = (6 378 136.7 ± 0.05) m.     

The system enstatite-pyrope at high pressures and temperatures and the mineralogy of the earth's mantle

In a diamond-anvil pressure cell coupled with laser heating, the system enstatite (MgSiO₃)-pyrope (3 MgSiO₃ · Al₂O₃) has been studied in the pressure region between about 100 and 300 kbar at about 1000°C using glass starting materials. The high-pressure phase behavior of the intermediate compositions of the system contrasts greatly with that of the two end-members. Differences between MgSiO₃ and 95% MgSiO₃ · 5% Al₂O₃ are especially remarkable. The phase assemblages β-Mg₂SiO₄ + stishovite and γ-Mg₂SiO₄ (spinel) + stishovite displayed by MgSiO₃ were not observed in 95% MgSiO₃ · 5% Al₂O₃, and the garnet phase, which was observed in 95% MgSiO₃ · 5% Al₂O₃ at high pressure, was not detected in MgSiO₃. These results suggest that the high-pressure phase transformations found in pure MgSiO₃ would be inhibited under mantle conditions by the presence even of small amounts of Al₂O₃ (?4% by weight). On the other hand, pyrope displays a wide stability field, finally transforming at 240–250 kbar directly to an ilmenite-type modification of the same stoichiometry. The two-phase region, within which orthopyroxene and garnet solid solutions coexist, is very broad. The structure of the earth's mantle is discussed in terms of the phase transformations to be expected in a simple mixture of 90% MgSiO₃ · 10% Al₂O₃ and Mg₂SiO₄. The seismic discontinuity at a depth of 400 km in the earth's mantle is probably due entirely to the olivine → β-phase transition in Mg₂SiO₄, with the progressive solution of pyroxene in garnet (displayed in 90% MgSiO₃ · 10% Al₂O₃) occurring at shallower depths. The inferred discontinuity at 650 km is due to the combination of the phase changes spinel → perovskite + rocksalt in Mg₂SiO₄ and garnet → ilmenite in 90% MgSiO₃ · 10% Al₂O₃. The 650-km discontinuity is thus characterized by an increase in the primary coordination of silicon from 4 to 6. A further discontinuity in the density and seismic wave velocities at greater depth associated with the ilmenite-perovskite phase transformation in 90% MgSiO₃ · 10% Al₂O₃ is expected.     

Determination of the Geopotential Scale Factor from TOPEX/POSEIDON Satellite Altimetry

The geopotential scale factor R _o = GM/W _o (the GM geocentric gravitational constant adopted) and/or geoidal potential Wo have been determined on the basis of the first year's (Oct 92 – Dec 93) ERS-1/TOPEX/POSEIDON altimeter data and of the POCM 4B sea surface topography model: R _o °=(6 363 672.58°±0.05) m, W _o °=(62 636 855.8°±0.05)m ² s ^–2 . The 2°–°3 cm uncertainty in the altimeter calibration limits the actual accuracy of the solution. Monitoring dW _o /dt has been projected.